3.3.2 The Derivative of the Square Root Function Flashcards Preview

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Flashcards in 3.3.2 The Derivative of the Square Root Function Deck (16):
1

The Derivative of the Square Root Function

• f(x) = √x is f'(x)=1/2√x
The derivative of is .
• To find the instantaneous rate of change of an object at a specific time, substitute the time into the derivative of the position function.
• To find the time when an object is moving a particular speed, set the derivative equal to that speed and solve for the independent variable.

2

note

- To find the instantaneous rate of change given the position function, start by finding the derivative.
- To find the derivative of the square root function, you will have to multiply the numerator and the denominator by the conjugate of the numerator.
- Evaluate the derivative at a specific time to find the instantaneous rate of change at that time.
- To find when an object is moving at a particular speed, set the derivative equal to that rate.
- Solve the derivative for the independent variable.

3

Suppose a particle's position is given by f(t)=√t+3,where t is measured in seconds and f(t) is given in centimeters. What is the velocity of the particle when t=1?

1/4 cm/sec

4

This limit represents the derivative of some function f at some number a. lim Δx→0 √2+Δx−√2 / ΔxWhat is f(x)?

f(x)=√x

5

Find the derivative of f(x)=√x/5.

f′(x)=1/2√5x

6

Suppose f(x)=√x.  What is the instantaneous rate of change in f when x=2?

1/2√2

7

Find the derivative of f(x)=3√x/4.

f′(x)=3/8√x

8

Suppose f(x)=√x^2+5. Find the equation of the line tangent to f(x)at (−2,3).

y−3=−2/3(x+2)

9

Find the derivative of f(x)=√x/4.

f′(x)=1/8√x

10

Suppose f(x)=√x+2. What is the slope of the line tangent to f when x=3?

m=1/2√5

11

Suppose f(x)=√2x−1. What is the slope of the line tangent to f when x=5?

m=1/3

12

Suppose a particle's position is given by f(t)=√t+3, where t is measured in seconds and f(t) is given in centimeters. At what time is the velocity of the particle equal to 1/4?

t = 1

13

Suppose a particle's position is given by f(t)=√2t+5,where t is measured in seconds and f(t) is given in centimeters. What is the velocity of the particle when t=2?

1/3 cm/sec

14

Suppose f(x)=√x−3.  What is the domain of f′(x)?

{x|x>3}

15

Suppose f(x)=√x+1. Find the equation of the line tangent to f(x)at (3, 2).

y−2=1/4(x−3)

16

Suppose a particle's position is given by f(t)=3√t^2+5,where t is measured in seconds and f(t)is given in centimeters. At what time is the velocity of the particle equal to 2?

t = 2

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